Actuarial Modeling of COVID-19 Insurance


CAUCHY –Jurnal Matematika Murni dan Aplikasi 
Volume 7(3) (2022), Pages 362-369 
p-ISSN: 2086-0382; e-ISSN: 2477-3344 

Submitted: January 04, 2022 Reviewed: July 23, 2022 Accepted: August 20, 2022 
DOI: http://dx.doi.org/10.18860/ca.v7i3.14999     

Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty*, Maulana Muhamad Arifin, Bagus Kurniawan, Sadam Laksamana 
Sukarno, Muhammad Teguh Prayoga 

Department of Mathematics, Faculty of Mathematics and Natural Sciences, 
 Universitas Brawijaya, Malang, Indonesia 

 
Email: mila_n12@ub.ac.id  

 

ABSTRACT  

The coronavirus disease (COVID-19) has spread to almost all countries in the world causing 
economic and financial crisis. Many researchers are interested in studying infectious diseases 
especially in dynamical models of COVID-19. Peng et al in 2020 studied the generalized SEIR 
(Susceptible-Exposed-Infected-Recovered) of COVID-19. We interested to develop their results to 
make financial arrangement. In this article, we provide an actuarial model of the COVID-19 
insurance based on the generalized SEIR model. We construct the dynamical models of premium 
and benefit based on generalized SEIR. Based on its dynamical model, we formulate the premium 
and the premium reserves on hospitalization and death benefits of the COVID-19 insurance by 
using equivalence principle.  This actuarial model is expected to able to help financial 
arrangements to cover losses due to the outbreak of COVID-19.  

Keywords:  premium; premium reserves; generalized SEIR; hospitalization benefit; death 
benefit  

INTRODUCTION 

The novel coronavirus-caused pneumonia 2019 (COVID-19) previously called 
2019-nCoV or SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2) first 
appeared in Wuhan in December 2019 and then spread rapidly throughout China [1]. 
Based on data on Woldometer (2021), this COVID-19 case has spread to almost all 
countries in the world [2]. This condition had a huge impact on the world economy, 
financial institutions in crisis [3]. Arfah et al. [4] studied a new strategy to solve the 
problem of the global financial crisis in the sharia aspect. From a financial point of view, a 
well-designed health care system that can reduce the financial impact of sudden 
outbreaks of a pandemic, such as soaring medical costs, hospital infrastructure, medical 
equipment, vaccination and quarantine. Then the insurance program is expected  to cover 
financial losses arising from disruptions in operation of regular businesses. By applying 
mathematical and actuarial techniques to model and measure financial risk, actuaries are 
expected to expand their expertise and tackle epidemics in the health care system. 

The mathematical modeling has been widely developed and analyzed as a 
consideration to determine the insurance premium (see [5], [6], [7]). Feng and Garrido 
[8] used the epidemic model to make financial arrangements.  They used the SIR 
(susceptible-infected-removed) model to study the infectious diseases. The class S 

http://dx.doi.org/10.18860/ca.v7i3.14999
mailto:mila_n12@ub.ac.id*


Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 363 

denoted a group of susceptible individuals to the certain diseases or virus. The class I 
denoted a group of individuals who are infected and capable of transmitting the disease. 
The individuals were excluded from the epidemic due to death or recovery through 
medical treatment are classified in class R. The dynamic model compartments as in [8] 
are given in Figure 1 below. 

 
Figure 1. Dynamical model of the SIR premium and benefit payment [8] 

 

The outbreak of COVID-19 has attracted researchers’ interest in studying infectious 
diseases. There are several research which studied the SIR model of the COVID-19 
epidemic (see [9] and [10]). However, in the development of the case, there is another 
factor influencing the spread of disease in COVID-19 cases, namely exposed individuals as 
in [11] and [12]. Peng et al. [13] and Aldila et al. [14] added some classes influencing the 
COVID-19 epidemic model. To characterize the outbreak of COVID-19 in Wuhan, Peng et 
al. [13] generalized the classical SEIR (susceptible-exposed-infected-removed) model by 
introducing seven classes, that is  {𝑆(𝑡), 𝑃(𝑡), 𝐸(𝑡), 𝐼(𝑡), 𝑄(𝑡), 𝑅(𝑡), 𝐷(𝑡)}  which represent 
the number of the susceptible cases, insusceptible cases, exposed cases, infective cases, 
quarantined cases, recovered cases and death case, respectively, at time 𝑡. The epidemic 
model for COVID-19 of [13] is given in Figure 2. 

 
Figure 2. Dynamical model of the generalized SEIR for COVID-19 [13] 

 

The total population is assumed constant, that is the summation of all classes, and the 
coefficient 𝛼, 𝛽, 𝛾 −1, 𝜃−1, 𝜆(𝑡), 𝜅(𝑡) represent the respective protection rate, infection rate, 
average latent time, average quarantine time, cure rate, and mortality rate. 

In this paper, the dynamical model of Peng et al. [13] will be generalized to 
determine actuarial calculation of COVID-19 insurance. In particular, our result improves 
the previous work due to Feng and Garrido [8]. The first one we construct the dynamical 
model of premium and benefit payment, and then we use the classical actuarial calculation 



Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 364 

to determine actual present value of benefit payment and premium payment, and also the 
premium reserves (see [15]-[20]). 

 

METHODS  

In this research, we develop the research methods into some steps. The first one, the 
Figure 2 is modified into actuarial concept, by adding the premium payment and benefit 
payment. The premium payment must be done by the population in class 𝑆, 𝐸, 𝐼, 𝑅, and 𝑃. 
The population in class 𝑄 have to get the hospitalization benefit, whereas the population in class 
𝐷 have to get the death benefit. From the new figure will be construct the ordinary 
differential equation of dynamical model. Based on the dynamical model will be 
constructed the premium rate and the premium reserve. The equivalence principle will 
be used to construct it. 

RESULTS AND DISCUSSION  

Dynamical Model of Premium and Benefits 

In this section, the compartment model in Peng et al. [13] will be generalized to 
dynamical model of premium payments for the COVID-19 policyholders and benefit 
payments by insurance companies. The compartments of the dynamical model are given 
in Figure 3.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 

Figure 3. The Dynamical model of premium dan benefit payments on generalized SEIR 
 

In this case the policyholder is assumed to be out of insurance after recovery. By [13], the 
compartment of the generalized SEIR model is denoted by following system of ordinary 
differential equations: 

Infective (I) 
𝛾 

𝛽 

Premium 

Payment  

𝜆(𝑡) 𝜅(𝑡) 

Premium 

Payment 

𝛼 

Recovered (R) 

Susceptible (S) Exposed (E) 

Insusceptible (P) Quarantined (Q) 

Insurance 

Death (D) 

𝜃 

Premium 

Payment 
Hospitalization 

Benefit 

Premium 

Payment 

Death 

Benefit 



Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 365 

𝑑𝑆(𝑡)

𝑑𝑡
= −𝛼𝑆(𝑡) − 𝛽

𝑆(𝑡)𝐼(𝑡)

𝑁
                                                                                                    (1) 

𝑑𝐸(𝑡)

𝑑𝑡
= −𝛾𝐸(𝑡) + 𝛽

𝑆(𝑡)𝐼(𝑡)

𝑁
                                                                                                   (2) 

𝑑𝐼(𝑡)

𝑑𝑡
 = 𝛾𝐸(𝑡) − 𝜃𝐼(𝑡)                                                                                                                (3) 

𝑑𝑄(𝑡)

𝑑𝑡
= 𝜃𝐼(𝑡) − 𝜆(𝑡)𝑄(𝑡) − 𝜅(𝑡)𝑄(𝑡)                                                                                    (4) 

𝑑𝑅(𝑡)

𝑑𝑡
= 𝜆(𝑡)𝑄(𝑡)                                                                                                                          (5) 

𝑑𝐷(𝑡)

𝑑𝑡
= 𝜅(𝑡)𝑄(𝑡)                                                                                                                         (6) 

𝑑𝑃(𝑡)

𝑑𝑡
= 𝛼𝑆(𝑡)                                                                                                                                (7) 

with given initial value 𝑆(0) = 𝑆0, 𝐸(0) = 𝐸0, 𝐼(0) = 𝐼0, 𝑄(0) = 𝑄0, 𝑅(0) = 𝑅0, 𝐷(0) =
𝐷0, 𝑃(0) = 𝑃0, and 𝑆0 + 𝐸0 + 𝐼0 + 𝑄0 + 𝑅0 + 𝐷0 + 𝑃0 = 𝑁. 

In actuarial approach, the probability of each class is defined by rasio of each class 
to the total population, then we now introduce the deterministic functions 
𝑠(𝑡), 𝑒(𝑡), 𝑖(𝑡), 𝑞(𝑡), 𝑟(𝑡), 𝑑(𝑡), and  𝑝(𝑡), represented as the fractions of the population in 
each of class 𝑆, 𝐸, 𝐼, 𝑄, 𝑅, 𝐷, and 𝑃, respectively. By dividing equations (1)-(7) by the 
constant total population size 𝑁, we have 

𝑠′(𝑡) = −𝛼𝑠(𝑡) − 𝛽𝑠(𝑡)𝑖(𝑡), 𝑡 ≥ 0                                                                                            (8) 
𝑒′(𝑡) = −𝛾𝑒(𝑡) + 𝛽𝑠(𝑡)𝑖(𝑡), 𝑡 ≥ 0                                                                                            (9) 
𝑖′(𝑡)  = 𝛾𝑒(𝑡) − 𝜃𝑖(𝑡), 𝑡 ≥ 0                                                                                                    (10) 
𝑞′(𝑡) = 𝜃𝑖(𝑡) − 𝜆(𝑡)𝑞(𝑡) − 𝜅(𝑡)𝑞(𝑡), 𝑡 ≥ 0                                                                         (11) 
𝑟′(𝑡) = 𝜆(𝑡)𝑞(𝑡), 𝑡 ≥ 0                                                                                                              (12) 
𝑑′(𝑡) = 𝜅(𝑡)𝑞(𝑡), 𝑡 ≥ 0                                                                                                             (13) 
𝑝′(𝑡) = 𝛼𝑠(𝑡), 𝑡 ≥ 0                                                                                                                   (14) 

𝑠(𝑡) + 𝑒(𝑡) + 𝑖(𝑡) + 𝑞(𝑡) + 𝑟(𝑡) + 𝑑(𝑡) + 𝑝(𝑡) = 1, 𝑡 ≥ 0                                             (15) 
with initial given value 𝑠(0) = 𝑠0, 𝑒(0) = 𝑒0, 𝑖(0) = 𝑖0, 𝑞(0) = 𝑞0, 𝑟(0) = 𝑟0, 𝑑(0) =

𝑑0, 𝑝(0) = 𝑝0, dan 𝑠0 + 𝑒0 + 𝑖0 + 𝑝0 = 1. 
 

Premium and Benefit Payments 

We assume that the premium payment of an infectious disease insurance plan in the 
form of continuous annuities from the susceptibles, insuspectible, infected, and exposed. 
It means the policyholder are commited to pay the premiums continuously as long as they 
remain in susceptibles, insuspectible, infected, and exposed classes. Otherwise, the 
insurance company will give the benefit if the policyholder are quarantined and death. 
Once the individual dies or recovery after quarantined process in hospital, the plan 
terminates immediately. 

By using the principles of International Actuarial Notation as mention in [8], the 
actuarial present value (APV) of each class for a 𝑡-year period is denoted by 

�̅��̅�|
𝑠 , �̅��̅�|

𝑒 , �̅��̅�|
𝑖 , �̅�

�̅�|
𝑞

, �̅��̅�|
𝑟 , �̅��̅�|

𝑑 , and �̅�
�̅�|
𝑝

.  To evaluate the annuity, we use the present value of 

payments due at time 𝑡, which is the discounted value of one monetary unit for a basic 
annuity. Then it is multiplied by the probability of making those payments and then 
integrate these APV for all payment times 𝑡. The detailed evaluations of annuities can be 
found in ([17] and 18]). 



Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 366 

By Figure 3, there are 2 benefits, i.e, hospitalization benefit  and death benefit.  The 
hospitalization benefit will be given to quarantined individual and death benefit will be 
given to death individual. The medical and hospitalization expenses are continuously 
reimbursed for each quarantined policyholder during the whole period of treatment. 
Hence, the total discounted value of a 𝑡-year annuity of hospitalization payments is can be 
descibed as follows 

�̅�
�̅�|
𝑞

= ∫ 𝑒−𝛿𝑥
𝑡

0

. 𝑞(𝑥) 𝑑𝑥,   𝛿 > 0                                                            (16) 

where 𝛿 is the discounting force of interest. When the policyholder is diagnosed with the 
infectious disease and hospitalized immediately, the medical expenses are to be paid 
immediately in a lump sum. Since its obligation is fulfilled, the insurance plan terminates. 
In actuarial mathematics, the payment of  a lump sum compensation can be analogized as 
whole life insurance. The APV of hospitalization benefit with lumpsum payment, denoted 
by �̅�

�̅�|
𝑞

, is defined by 

�̅�
�̅�|
𝑞

 = ∫ 𝑒−𝛿𝑥
𝑡

0

. 𝜃𝑖(𝑥) 𝑑𝑥 = 𝜃�̅��̅�|
𝑖                                                 (17) 

since 𝜃𝑖(𝑡) denotes the probability of being newly quarantined at time 𝑡. By the same 
concept of lumpsum payment of hospitalization benefit, the APV of death benefit is given 
by 

�̅��̅�|
𝑑  = ∫ 𝑒−𝛿𝑥

𝑡

0

. 𝜅(𝑥)𝑞(𝑥) 𝑑𝑥                                                        (18) 

since the probability of being newly death at time 𝑡 is 𝜅(𝑡)𝑞(𝑡). 
As in the previous section, there are 4 classes must pay the premium, then the total 

discounted value of a 𝑡-year annuity premium of payments is given by 

�̅��̅�|
𝑠 + �̅�𝑡|

𝑒 + �̅�𝑡̅|
𝑖 + �̅�

�̅�|
𝑝

= ∫ 𝑒−𝛿𝑥
𝑡

0

. (𝑠(𝑥) + 𝑒(𝑥) + 𝑖(𝑥) + 𝑝(𝑥)) 𝑑𝑥                      (19) 

In this section, the compartment model in Peng et al. [13] is generalized to dynamical 
model of premium payments for the COVID-19 policyholders and benefit payments by 
insurance companies.  

Premium Rate and Premium Reserves 

The policy shall be analized with an infinite term for mathematical convenience. The 
premium based on an infinite term can be used to estimate the cost of insurance for 
relatively long policy. Then the equation in the previous section must be applied for 𝑡 tend 
to infinity. 

 
Proposition 1 
In the generalized SEIR model  (8)-(11), and (14), the following inequality holds 

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�∞̅|

𝑝
+ �̅�∞̅|

𝑞
=

1

𝛿
(1 − ∫ 𝑒−𝛿𝑥 (𝜆(𝑥) + 𝜅(𝑥))𝑞(𝑥)𝑑𝑥

∞

0

)            (20) 

 
Our study is based on one of three principles in [17] and almost used in ([15] - [20]), 

i.e., the Equivalence Principle for determination of level premium is given by 
𝐸[present value of benefits] = 𝐸[present value of benefit premium]                     (21) 



Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 367 

 
Therefore, by using the equations (16), (19), and equivalence principle with an infinite 
term, the level premium for a unit annuity claim payment plan of hospitalization benefit 
is given by 

�̅�(�̅�∞̅|
𝑞

) =
�̅�∞̅|

𝑞

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�

∞̅|
𝑝            

By equation (20) we then have the following 

�̅�(�̅�∞̅|
𝑞

) =
�̅�∞̅|

𝑞

1

𝛿
(1 − ∫ 𝑒−𝛿𝑥 (𝜆(𝑥) + 𝜅(𝑥))𝑞(𝑥)𝑑𝑥

∞

0
) − �̅�

∞̅|
𝑞

                    

The net level premium of hospitalization benefit with lumpsum payment for the 

infinite term insurance plan is denoted by �̅�(�̅�∞̅|
𝑞

). By equations (17), and (19)-(21) for 

infinite term we then have 

�̅�(�̅�∞̅|
𝑞

) =
�̅�∞̅|

𝑞

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�

∞̅|
𝑝 =

𝜃�̅�∞̅|
𝑖

1

𝛿
(1 − ∫ 𝑒−𝛿𝑥 (𝜆(𝑥) + 𝜅(𝑥))𝑞(𝑥)𝑑𝑥

∞

0
) − �̅�

∞̅|
𝑞

      

In fact, the COVID-19 insurance is a combination of the hospitalization and death 
insurances due to COVID-19. Then the net level premium of death benefit and 
hospitalization claim for the infinite term insurance plan is denoted by 

 

�̅�(�̅�∞̅|
𝑞

+ �̅�∞̅|
𝑑 ) =

�̅�∞̅|
𝑞

+ �̅�∞̅|
𝑑

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�

∞̅|
𝑝 =

�̅�∞̅|
𝑞

+ ∫ 𝑒−𝛿𝑥
∞

0
. 𝜅(𝑥)𝑞(𝑥) 𝑑𝑥

1

𝛿
(1 − ∫ 𝑒−𝛿𝑥 (𝜆(𝑥) + 𝜅(𝑥))𝑞(𝑥)𝑑𝑥

∞

0
) − �̅�

∞̅|
𝑞

 

Meanwhile, the net level premium of death benefit and hospitalization claim with 
lumpsum payment for the plan of an infinite term insurance is given by 

�̅�(�̅�∞̅|
𝑞

+ �̅�∞̅|
𝑑 ) =

�̅�∞̅|
𝑞

+ �̅�∞̅|
𝑑

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�

∞̅|
𝑝 =

𝜃�̅�∞̅|
𝑖 + + ∫ 𝑒−𝛿𝑥

∞

0
. 𝜅(𝑥)𝑞(𝑥) 𝑑𝑥

1

𝛿
(1 − ∫ 𝑒−𝛿𝑥 (𝜆(𝑥) + 𝜅(𝑥))𝑞(𝑥)𝑑𝑥

∞

0
) − �̅�

∞̅|
𝑞

 (22) 

We consider the net level premium, the total premium and the total benefit in order 
to obtained the premium reserves. In actuarial sciences, the premium reserve is very 
important to determine the ability of the insurance company to pay the claim of 
policyholders. There are some methods to determine the premium reserves. One of them 
is retrospective method, the detail of this method can be found in [19]. By ordinary 
differential equations in [4], where �̅�(𝑡) denotes accumulated premium reserves at time 
𝑡 with lumpsum payment, we thus have 

�̅�′(𝑡) = �̅�(�̅�∞̅|
𝑞

+ �̅�∞̅|
𝑑 )(𝑠(𝑡) + 𝑒(𝑡) + 𝑝(𝑡) + 𝑖(𝑡)) − (𝜃𝑖(𝑡) + 𝜅(𝑡)𝑞(𝑡)) + 𝛿�̅�(𝑡) 

= (
�̅�∞̅|

𝑞
+ �̅�∞̅|

𝑑

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�

∞̅|
𝑝 ) (𝑠(𝑡) + 𝑒(𝑡) + 𝑝(𝑡) + 𝑖(𝑡)) − (𝜃𝑖(𝑡) + 𝜅(𝑡)𝑞(𝑡)) + 𝛿�̅�(𝑡) 

Let us define 𝑓(𝑡) = (
�̅�∞̅̅̅|

𝑞
+�̅�∞̅̅̅|

𝑑

�̅�∞̅̅̅|
𝑠 +�̅�∞̅̅̅|

𝑒 +�̅�∞̅̅̅|
𝑖 +�̅�

∞̅̅̅|
𝑝 ) (𝑠(𝑡) + 𝑒(𝑡) + 𝑝(𝑡) + 𝑖(𝑡)) − (𝜃𝑖(𝑡) + 𝜅(𝑡)𝑞(𝑡)) 

we thus have 
�̅�′(𝑡) − 𝛿�̅�(𝑡) = 𝑓(𝑡) 

By multiplying both sides by 𝑒−𝛿𝑡 , yields 

�̅�(𝑡) = (∫ 𝑒−𝛿𝑥 𝑓(𝑥)

𝑡

0

𝑑𝑥) . 𝑒𝛿𝑡 + �̅�(0). 𝑒𝛿𝑡     

or equivalently, 



Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 368 

�̅�(𝑡) = (∫ 𝑒−𝛿𝑥 (
�̅�∞̅|

𝑞
+ �̅�∞̅|

𝑑

�̅�∞̅|
𝑠 + �̅�∞̅|

𝑒 + �̅�∞̅|
𝑖 + �̅�

∞̅|
𝑝 ) (𝑠(𝑥) + 𝑒(𝑥) + 𝑝(𝑥) + 𝑖(𝑥))

𝑡

0

− (𝜃𝑖(𝑥) + 𝜅(𝑥)𝑞(𝑥)) 𝑑𝑥) . 𝑒𝛿𝑡 + �̅�(0). 𝑒𝛿𝑡                                                    (23)  

From equation (23), the amount of the premium reserve at time 𝑡 depends on the total 
premium, the death benefit and quarantined benefit, and also the initial value of the 
premium reserve. 

CONCLUSIONS 

The COVID-19 insurance by considering the generalized SEIR model was assumed that 
the recovery individuals not involved in premium payment since the policyholder who 
has been quarantined in the hospital and claims the benefit payment then the insurance 
plan terminates. Therefore, the total premium of payment are depend on class  𝑆(𝑡), 𝐸(𝑡), 
𝐼(𝑡), and 𝑃(𝑡). Meanwhile, the total benefit of payment are depend on class 𝑄(𝑡) and 𝐷(𝑡). 
By using equivalence principle, the net level premium is the ratio of actuarial present 
value of benefits to actuarial present value of premiums. Hence we get the premium 
reserve by restrocpective approach. 

ACKNOWLEDGMENTS  

This research is supported by the Doctoral Grant No. 1631/UN10.F09/PN/2021 at 
Mathematics and Natural Sciences Faculty, Universitas Brawijaya. 

REFERENCES 

 
[1] C. Huang, Y. Wang, X. Li, L. Ren, J. Zhao, Y. Hu, Li. Zhang, G. Fan, J. Xu, X. Gu, Z. Cheng, 

T. Yu, J. Xia, Y. Wei, W. Wu, X. Xie, W. Yin, H. Li, M. Liu, Y. Xiao, H. Gao, L. Guo, J. Xie, G. 
Wang, R. Jiang, Z. Gao, Q. Jin, J. Wang, and B. Cao. Clinical features of patients infected 
with 2019 novel coronavirus in Wuhan, China. The Lancet, vol.395, Issue 10223, pp. 
497-506, 2020. 

[2] Woldometer. Report coronavirus cases. Retrieved March 17, 2021, from 
https://www.worldometers.info/coronavirus/#countries, 2021. 

[3] M. F. Sattar, S. Khanum, A. Nawaz, M. M. Ashfaq, M. A. Khan, M. Jawad, and W. Ullah. 
Covid-19 Global, Pandemic impact on World Economy. Technium Social Sciences 
Journal. vol. 11, pp.165-179, 2020. 

[4] A. Arfah, F. Z. Olilingo, F. Zain, S. Syaifuddin, D. Dahliah, N. Nurmiati, and A. H. K. 
P.Putra. Economics During Global Recession: Sharia-Economics as a Post COVID-19 
Agenda. Journal of Asian Finance, Economic and Business, vol.7, no. 11, pp.1077-1085, 
2020. 

[5] B. L. Jones. Actuarial Calculations Using a Markov Model. Transactions of the Society 
of Actuaries, vol. 46, pp.227–250, 1994. 

[6] N. Jia and L. Tsui. Epidemic Modelling using SARS as a Case Study. North American 

Actuarial Journal, vol. 9, no.4, pp. 28 – 42, 2005. 

https://www.worldometers.info/coronavirus/#countries


Actuarial Modeling of COVID-19 Insurance 

Mila Kurniawaty 369 

[7] Canadian Institute of Actuaries, “Considerations for the Development of a Pandemic 

Scenario”. Canadian Institute of Actuaries, Committee on Risk Management and 

Capital Requirements. Research Paper 209095, 2009. 

[8] R. Feng and J. Garrido. Actuarial Applications of Epidemiological Models. North 
American Actuarial Journal, vol. 15, no.1, pp. 112-136, 2012. 

[9] M. Batista. Estimation of the Final Size of The Coronavirus Epidemic by the SIR 
Model, preprint, 2020. 

[10] I. Cooper, A. Mondal, and C. G. Antonopoulos. A SIR Model Assumption For The 
Spread Of COVID-19 In Different Communities. Chaos, Solitons and Fractals, vol. 139, 
2020. 

[11] B. Tang, N.L. Bragazzi, Q. Li, S. Tang, Y. Xiao, and J. Wu, J. An updated estimation of 
the risk of transmission of the novel coronavirus (2019-nCoV). Infectious Disease 
Modelling. vol. 5, pp. 248-255, 2020. 

[12] T. Zhou, Q. Liu, Z. Yang, J. Liao, K. Yang, W. Bai, X. Lu, and  W. Zhang. Preliminary 
predistion of the basic reproduction number of the Wuhan novel coronavirus 2019-
nCoV. Journal of Evidence-based Medicine, vol. 13, no.1, 2020. 

[13] L. Peng, W. Yang, D. Zhang, C. Zhuge, and  L. Hong. Epidemic analysis of COVID19 in 

China by dynamical modeling. arXiv preprint arXiv:2002.06563, 2020. 

[14] D. Aldila, S. H. A. Khoshnaw, E. Safitri, Y. R. Anwar, A. R. Q. Bakry, B. M. Samiadji, D. 
A. Anugerah, M. F. Alfarizi, I. D. Ayulani, and S. N. Salim. A mathematical study on the 
spread of COVID-19 considering social distancing and rapid assessment: The case of 
Jakarta, Indonesia. Chaos, Solitons and Fractals, vol.139, 2020. 

[15] H. U. Gerber. Life Insurance Mathematics. Springer, Berlin, Heidelberg, 1997. 
[16] N. L. Bowers, H. U. Gerber, J. C. Hickman, D A. Jones, and C. J. Nesbitt. Actuarial 

Mathematics. The Society of Actuaries, 1997. 
[17] R. J. Cunningham, T. N.  Herzog, and R. L. London. Model fo Quantifying Risk, 2nd ed, 

ACTEX Publication Inc., Winsted, 2006. 
[18] D. C. M. Dickson, M. R. Hardy, and H. R. Waters. Actuarial Mathematics for Life 

Contingent Risks, 2nd ed, Cambridge University Press, United Kingdom, 2003. 
[19] R. K. Sembiring. Buku Materi Pokok Asuransi I. Karunika Universitas Terbuka. 

Jakarta, 1986. 
[20] I. Catarya. Buku Materi Pokok Asuransi II. Karunika Universitas Terbuka. Jakarta, 

1988.